1

Proceedings of the First Conference on
Asian and Pacific Coastal Engineering 2001
October 18-21, 2001, Dalian, China, pp. 1 – 24.

A NEW APPROACH TO BEACH MORPHOLOGY WITH THE FOCUS ON
SUSPENDED SEDIMENT TRANPSORT
Yoshimi Goda1

ABSTRACT: An assessment of the roles of various modes of sediment motions on longshoretransport is presented. Then a literature survey is made for overviewing the research efforts onlongshore sediment transport problems with a focus on suspended load. The past efforts with theemphasis on bed load transport are said to have the roots in pioneering works by Einstein andBagnold. However, many field measurements on suspended sediment concentration havedemonstrated the importance of suspended sediment in the analysis and prediction of longshore
sediment transport. A macroscopic model for estimating sediment pickup rate by random
breaking waves is introduced with its extension to the prediction of beach morphological changes.

1. Introduction
Beach morphology has been puzzling people since old days. Shorelines advance and/or retreat
beyond the expectation of local people. Excessive retreat of shorelines or beach erosion
endangers the living of people there. Unexpected deposit of sand on a beach may cause shoalingof a harbor nearby that leads to the loss of function to accommodate ships in the harbor.
Scientific studies of sediment transport that causes morphological changes of beaches began
in the 1940s. More than half a century has elapsed in our efforts to understand the phenomenonof sediment transport by waves and currents. Although thousands of papers and reports have been
published in the past, we are still unable to predict the shoreline changes with confidence. The
author believes that the main reason of our incapability is our failure in correctly evaluating therole of suspended sediment energized by breaking waves in the surf zone.
Table 1 lists an assessment on the roles of various modes of sediment motions on longshoretransport, which causes the morphological changes of beaches in the time span of months,
seasons, and years. The cross-shore movement of sediment that causes beach profile changes in a
few days is not discussed in the present paper, because the onshore and offshore transports tend
to cancel out in a long time span. The assessment of the relative importance of the modes ofvarious sediment motions represents the personal view of the author, in the situation thatquantitative data making such an assessment is insufficient. The author would welcome thecomments of other scientists and engineers on this assessment from different viewpoints.
The sediment transport in rivers and coasts has two modes: i.e., bed load and suspended loadtransports. The bed load transport occurs in the mode of either individual particles motions or
1

Professor Emeritus at Yokohama National University, ECOH Corporation, 2-6-4 Kita-Ueno, Taito-ku
Tokyo 110-0014, Japan. goda@ecoh.co.jp

2sheet flow movement. Presently the mechanism of the former mode including formation of sandripples has been well clarified by many research efforts, while the phenomenon of sheet flow of
sediment has become somewhat known. The extent of their contributions to the longshoretransport needs to be scrutinized, however. Probably they are playing a major role in cross-shore
sediment transport, but individual sediment particles in the transport mode of bed load would notcontribute much to the longshore sediment transport. The sheet flow mode may exercise amedium influence on longshore transport.
Table 1. Tentative assessment of the roles of longshore sediment transport modes
Mode
Bed load:particles
sheet flow
Suspension: from sand ripples
by breakers

Present statealmost known
somewhat known
almost known
unknown

Total contribution
small
mediumlittledominant

Sediment particles are put in suspension by two driving forces. One is the shear stress ofoscillating flows acting on the bed layer, and the other is the vertical momentum of water jets
produced by breaking waves. Sediment suspension from the crests of sand ripples is a typicalexample of the former, and it has been studied quite well. However, the total quantity oflongshore transport of this type of suspended sediment is thought to be very small compared withthat of sediment suspended by breaking waves. The importance of sediment suspension bybreaking waves is readily understood when we look down the sea surface from a pier extending
through the surf zone; we can observe a burst of sediment cloud rising up in the water after aplunging breaker movers out toward the beach. The sediment cloud slowly moves alongshore
within the surf zone, carrying a large amount of suspended load.
There are some reports that suspended sediment rather than bed load dominates longshoretransport, especially during stormy conditions. Nevertheless, quantitative analysis of sedimentsuspension by breaking waves has not succeeded yet because of the complexity of phenomena
involved. The majority of studies on sediment transport problems have mainly addressed to the
topics of bed load and sediment suspension from sand ripples, by detouring the tough assignmentof solving the mystery of sediment suspension by breaking waves. It is now the time to focus ourresearch efforts on the above task so that we can make a breakthrough in the riddle of beachmorphology.
In the present paper, an overview of the past research efforts on sediment transport problems
will be made from the viewpoint why the phenomenon of sediment suspension by breaking
waves has not been paid due attention. Then a macroscopic model by Katayama and Goda (1999,
2000) will be introduced with its extension to the prediction of beach morphological changes.

2. Overview of Past Research Efforts on Sediment Transport Problems
2.1 EARLY STAGE STUDIES WITH METHODOLOGY OF RIVER SEDIMENT ANALYSISThe problem of beach erosion occurred at many places in the world from time to time, but
American people seem to have the keenest concern on conservation of beaches for summer resort.
Upon the demand of many people, the U.S. Army Corps of Engineers created the Beach Erosion

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Board in the early 1930s to deal with severe beach erosion problems along the American
coastline. After World War II, the U.S. Navy also found interests in wave-related problems. For
one of the projects commissioned to University of California, Berkeley, Einstein (1948) gave asuggestion for the direction of approach to be taken for the study on beach sand movements bywaves, saying that the concept of river sediment transport can be extended to beach sandmovements even though a river flows in one direction while beach sands are exposed tooscillatory flows of wave orbital motions.
Einstein had established his famous formula on bed load transport in rivers in 1942. His
formula was based on statistical concept with dimensional analysis. Later Kalinske (1947)
augmented the Einstein formula by giving more physical reasoning. Both of them had recognized
the necessity to include the suspended load into the total transport, but they analyzed the bed loadtransport only, probably because of difficulty in deriving any generalized conclusion on theamount of suspended load.
In the U.K., Bagnold (1946) initiated investigations on the motion of sand by waves; he had
been famous for his experiments on impulsive breaking wave force on a vertical wall as well as
his pioneering work on blown sand. He immersed a swinging, arc-shaped cradle, hanged from theceiling, in a water tank. By changing the amplitude and frequency of swinging motion of thecradle, he created oscillating water flows relative to the surface of cradle. Bagnold then placed alayer of sand on the cradle and observed the motion of sand particles by oscillating water flows.
The threshold velocities for initiation of particle motions, formation of sand ripples, andsuspension of sand particles from sand ripples were thus measured and recorded. Another methodof creating oscillating flows relative to a sand layer is to reciprocate a horizontal plate with sandon top of it in a water tank through a piston-motion mechanism. This method was used byManohar (1955) for the study of threshold velocities of sand motions in a manner similar as
Bagnold’s study.
An early laboratory study of sand movement by waves was reported by Scott (1954), whocarried out many tests at University of California, Berkeley. A few years later, a group of
researchers at the Massachusetts Institute of Technology began a series of detailed measurementson the wave-induced motion of particles on slopes. Eagleson and Dean (1961) summarized theirfindings on the vertical distribution of net velocity near the bed, the drag coefficient of sedimentparticles on bed, etc.
2.2 MECHANISMS OF SAND MOTIONS UNDER WAVE ACTIONS
2.2.1 Incipient Motions of Sediment Particles by Oscillating Flows
Studies on sand particle motions in the early stage stimulated interests of researchers on the
incipient motions of sediment particles by oscillating flows. To facilitate the laboratory experiments, Lungren and Sorensen (1957) invented a pulsating water tunnel, which later becamefavorite equipment in many coastal engineering laboratories in the world.
The threshold of incipient motions of sediment particles is mostly expressed in terms of theShields number, which normalizes the critical shear stress for driving particles into reciprocating
motions. The so-called Shields curve, i.e., plotting of the threshold Shields number against the
Reynolds number (defined by the shear velocity and the particle diameter), has been applied bymany researchers to their laboratory data. Furthermore, Larsen et al. (1981) reported the resultsof ocean measurements in which the threshold of fine sediment suspension from the sea bottomof 75 to 90 m deep by wave actions was well described by the Shields curve.

4However, Hallermeier (1980) analyzed ten sets of laboratory data by various investigatorsand concluded that the Shields curve is not suitable for describing the threshold of incipient
sediment motions by oscillating flows. Instead, he proposed two empirical formulas for thecritical orbital velocity, one for fine grains under high-frequency oscillations and the other forcoarse grains under relatively low-frequency oscillations. A recent paper by You (2000) also
discusses the threshold wave orbital velocity for initiation of sand particle motions in a similar
fashion.
2.2.2 Sediment Suspension by Shear Stress from Bed Layer
As the shear stress acting on sediment particles by wave motions increases, ripples appear on thesurface of sand layer on the bottom. With a further increase in the shear stress or orbital velocity,
sediment particles are put into suspension from the crests of sand ripples. Then suspended
sediment is moved upward by turbulence while being pulled down by gravity. The sedimentconcentration is densest near the bed and thinnest near the surface. The time-averaged vertical
distribution of sediment concentration is governed by the strength of turbulent eddy viscosity andthe settling velocity of sediment in suspension.
There have been many studies on the concentration of sediment suspended by wave actions;some made detailed experiments in oscillating water tunnels as well as in wave flumes, whileothers measured sediment concentrations in the sea. Das (1972) gave a review of early studies onsuspended sediment, the amount of which was mostly measured from water samples taken bysuction. Sleath (1982) is one of earlier investigators who made use of phototransistors to measure
the concentration of sediment. Nowadays, many optical backscatter sensors and acoustic sensors
are employed to monitor temporal variations of sediment concentrations, even though someresearchers favor the method of water sampling by suction. Nielsen (1984) used a speciallydevised water sampler for his field measurements in the nearshore zone. Black and Rosenberg(1994) compared optical and pump-sampling techniques with conclusions that the efficiency ofpump in trapping sediment may be affected by the strength of ambient turbulent eddies and the
response of optical backscatter sensors is strongly dependent on grain size.
The suspended sediment concentration near the bed is in the order of 1 g/l and decreases
rapidly to the order of 0.001 g/l as the height from the bed increases, when no wave breaking
takes place; e.g., Van Rijn et al. (1993). Nielsen (1986) gave a formula for the concentration at
the sea bottom as being proportional to the cube of a Shields parameter. The vertical distributionof suspended sediment concentration in waves can be calculated by solving the diffusion
equation. Fredsoe et al. (1985) demonstrated several results of numerical calculations that fit
quite well to laboratory data. Suspension of sediment from the crests of sand ripples can now be
simulated numerically. Asp Hansen et al. (1994) has presented a successful example using a
discrete vortex model.
Several field measurements have revealed the phenomenon of rapid rises of suspended
sediment concentration near the seabed, especially when conspicuous wave grouping is present;e.g., Hanes and Huntley (1986), and Williams et al. (1996). The transport of suspended sedimentis the product of concentration and flow velocity. Because the concentration fluctuates incorrelation with the flow components of wave motions, long-period motions, and mean currents,
the cross-shore transport rate must be calculated by integrating the instantaneous product ofconcentration and velocity instead of the product of the mean concentration and the mean
velocity, as demonstrated in the field data analysis by Osborne and Greenwood (1992). In thecase of longshore sediment transport rate, however, Jaffe and Sallenger (1992) found no clear

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correlation between the suspended sediment concentration and the longshore current velocity sothat the longshore transport rate can be calculated with the product of their means.
2.2.3 Sheet Flow of Sediment on Seabed
In the inner surf zone where intensive wave breaking is taking place, sand ripples on the seabeddisappear and sediment particles move en masse. This is called the sheet flow of sediment.
Ribberink and Al-Salem (1995) reported quite detailed measurements of sediment concentrationin the sheet flow layer in a large oscillating water tunnel. They devised a special sheet flow
sensor using an electro-resistance probe, and measured the temporal variation of sedimentconcentration. Within the layer of several millimeters below the surface, sediment particles are
fluidized from their static state of deposition and then return to the static state with the phases ofwave motions; their concentration periodically varies in the range of 800 to 1600 g/l. Above thesheet flow layer, the sediment moves in suspended state. Its concentration rapidly decreased fromabout 10 to 100 g/l on the bottom to 0.1 g/l or less at the height of about 5 cm.
2.3 SEDIMENT SUSPENSION IN THE SURF ZONE
2.3.1 Field Measurement of Suspended Sediment in the Surf Zone
The suspended sediment by nonbreaking waves exists only near the seabed with little
concentration in the water column as a whole. When waves break, however, suspended sedimentof high concentration rises up in mid-water and near the surface.
Field measurements of suspended sediment concentration had been made in many countries
since the 1950s. Among them, Fairchild (1972) succeeded in obtaining more than 800 data in thesurf zone at various elevations from the seabed to mid-depth. He moved a tractor-mounted pumpsampler along a pier extending from the shore; he utilized one pier at Ventnor in New Jersey andanother at Nags Head in North Carolina. The maximum concentrations ranged up to 2.6 g/l at
Ventnor and 4.0 g/l at Nags Head. The median diameter of suspended sediment was in the rangeof 0.12 to 0.20 mm. While the data by Fairchild gave an overall view of suspended sediment in
the surf zone, they were not well correlated with wave data and no simultaneous current
measurements were taken.
Since the 1970s, many field campaigns have been conducted in a more systematic way.
Kana and Ward (1980) reported the first systematic measurements of sediment concentrations
and current velocities along the CERC pier at Duck. They commented “the sediment concentrations ranged over 3-1/2 orders of magnitude from approximately 0.05 g/l to over 10.0 g/l withhighest concentrations in the inner surf zone and near the bed.” Then with introduction of opticalbackscatter sensors, it became clear that bursts of suspended sediment occur intermittently withthe peak concentration more than 20 g/l. Beach and Sternberg (1988) reported that suchsuspension events are correlated with infragravity waves of 30 to 300 s in period. Nadaoka et al.
(1988a) attributed suspension events to the three-dimensional large-scale eddies that were
produced by plunging breakers. Nadaoka et al. (1988b) further reported field measurements ofsuch eddies and their relationship with sediment suspension. Jaffe and Sallenger (1992) observedthat suspension events occurred in every 1 to 2 minutes with the concentration being one order ofmagnitude greater than the rest of time. Although the suspension events occupied less than 10%of the observation time, they contributed to the increase of mean concentration by 15% to 55%.
Black et al. (1995) presented several records of the suspended sediment of high-density clouds

6with explanation how they moved back and forth around the sensors in relation with the wave
motions. Miller (1999) also demonstrates records of suspension events with high-concentration
sediment reaching to near the water surface.
2.3.2 Large-Scale Laboratory Measurements of Suspended Sediment in the Surf Zone
Sediment suspension by breaking waves has also been investigated in very large wave flumes
with H1/3 exceeding 1.0 m. Dette and Ulizcka (1986) presented the earliest results of large-scale
tests. Dally and Barkaszi (1994), Roelvink and Reniers (1995), and Shimizu et al. (1996) reported
the test results of similar magnitude. A recent report by Peters and Dette (1999) expresses thevertical distribution of suspended sediment concentration in an exponential decay function as an
approximation, i.e.,c ( z ) = c0 e − az(1)where c(z) is the time-averaged concentration, c0 denotes the reference concentration on the bed,
and a represents the decay parameter. According to Peters and Dette (1999), c0 is around 10 g/l
and the value of a comes down to 2 m-1 in the inner surf zone, indicating nearly uniform
distributions.
Suspension events are evidently caused by breaking waves as demonstrated by Nadaoka etal. (1988a, 1988b). The role of breaking waves in sediment suspension has also been exhibited innumerical simulations by Pedersen et al. (1995), who used a discrete vortex model in analyzing
the velocity field in the surf zone. They obtained a good agreement of sediment concentration
with the measurement by Dette and Ulizcka (1986).
2.4 LONGSHORE SEDIMENT TRANSPORT FORMULAS
2.4.1 CERC Formula
Our capability in predicting beach changes solely depends on the reliability of sediment transport
formula. In the early days, the amount of total longshore sediment transport was estimated fromthe volumetric change of beach and berm in the coast where longshore sediment transport was
impounded by some barrier such as a jetty or others. The longshore transport rate was thencorrelated with the longshore component of wave energy flux during the period in which theamount of longshore sediment transport was estimated. Through accumulation of many data atvarious coasts, the so-called CERC formula (USACE 1984) was evolved. Its volumetricexpression is as follows:

K H b2 ( c g ) b(2)
sin α b cos α b
8 s (1 − λ )where K denotes the constant of the CERC formula being 0.385 on the average, H denotes thesignificant wave height H1/3, cg is the group velocity, α stands for the wave angle, the subscript b
denotes the value at the breaking point, s is the density ratio of sediment to water (s = ρ s / ρ ) ,and λ represents the void ratio of sediment in situ being about 0.4. When the root-mean-squarewave height Hrms is used, then the constant K takes the value 0.77.
The reliability of the CERC formula for making prediction of beach morphology has been
discussed over many years. Greer and Madsen (1978) is one of early reviewers, who recom-

qtotal =7mended the formula to be used for the order estimate only. The focus of discussion is the value of
constant K. While K is thought to be affected by the grain size, Komar (1988) could not find aclear relationship because of large scatter of field data. However, Del Valle et al. (1993)
supported the grain-size dependency of K with the field data of coarse sand coast with the grain
size up to 1.5 mm, and presented the following empirical relationship:

K = 0.8 exp[−2.5d ](3)where d is the grain size in millimeters. Schooness and Theron (1994) calculated the K value formany field data by grouping them with grain size. For the group with grain size smaller than 1
mm, the mean of K was 0.41, but for the group with grain size larger than 1 mm the mean was
0.01, although the effect of grain size could not be revealed within the two groups. A recent paper
by Van Wellen et al. (2000) also used the K value of 0.07 to fit the data on shingle beaches intheir assessment of various longshore transport formulas.
In addition to the CERC formula, several formulas have been proposed to evaluate the total
rate of longshore transport across the shore. The formula by Kamphuis (1991) is a representative
example. Schooness and Theron (1996) calibrated 52 formulas with 273 data points andconcluded the Kamphuis formula being the most reliable, although Van Wellen et al. (2000)
disagree with them, saying that their field database is biased towards a certain group ofenvironmental parameters.
2.4.2 Energetics Model by Bailard
Many sediment transport formulas are dedicated to predict the local transport rate. When
combined with the longshore current prediction and/or measurements, they yield the estimates of
total longshore sediment transport rate. Bayran et al. (2000) calibrated six sediment transport
formulas with the field measurement data of longshore currents and suspended sedimentconcentrations at various elevations along the CERC Field Research Facility (pier) at Duck. The
data of three experiments named DUCK 85, SUPERDUCK, and SANDYDUCK were analyzed
to yield the cross-shore distribution of longshore transport rate. The local transport rate formulas
include those by Bijker (1971), Bailard (1981), Watanabe (1992) and others. These formulas
comprise the bed load and suspended sediment transports evaluated mostly with the concept ofshear stress acting on the seabed.
Comparison between the field data and predictions was made of the cross-shore profiles of
local longshore transport rate as well as the whole data points. Most of predictions were in therange of 1/5 to 5 times the measurements, but some data were outside this range and the fractionof outside data among the whole was 4% to 38% depending on the formulas and wave
conditions; thus the performance of the prediction formulas was only fair.
Among the six formulas, the Bailard formula deserves explanations because it is based on
the energetics concept proposed by Bagnold (1963, 1966), who recommended use of the fluid
power rather than the shear stress as the driving force of sediment transport. According toBayram et al. (2000), the Bailard equation is expressed as follows:q = 0.5 ρ f w u 03

eb
es
 δV

+ δ V3  + 0.5ρ f w u 04
δ V u 3*ρρ
( ρ s − ρ ) g tan γ  2
(
−
)
gw

s
f

(4)

The notations in Eq. 4 are defined as follows: eb and es denotes the bed load and suspended load
efficiency factors (fraction of energy dissipation spent to sediment transport), respectively, fw is8

the wave friction factor, g is the acceleration of gravity, u0 represents the amplitude of wave
orbital velocity at the bed, u3* is the cubic velocity moment, wf stands for the sediment settling
velocity, δ V expresses the ratio of longshore current velocity to u0, γ is the wave heightparameter, and ρ and ρ s are the densities of water and sediment, respectively. Equation 4 is a
simplified version of the original equation by Bailard, who used the internal angle of friction of
the sediment φ instead of the parameter γ in the denominator of the first term in the right-handside of Eq. 4.
As for the constant values, Bailard (1981) gave the least squares estimates of eb and es as
0.21 and 0.025, respectively, but later recommended the values of eb = 0.13 and es = 0.032(Bailard, 1984) when he proposed Eq. 5 below. In the reference by Bayram et al. (2000),
however, they listed the values of eb = 0.1, es = 0.025, and tan γ = 0.63.
Bailard (1984) applied his formula to examine the parameters involved in the K value of the
CERC formula. By finding the coefficient values best fitting to field and laboratory data, hederived the following equation; the original constant values are halved because of the use ofsignificant wave height in Eq. 4:(5)
K = 0.025 + 1.3 sin 2 2α b + 0.0035u 0b / w fThis is an explicit inclusion of the grain size effect (settling velocity) into the longshore sedimenttransport formulas. The settling velocity of sediment can be estimated with the formula derived
by Rubey (1933) who worked on the problems of sediment motion on riverbeds, i.e.,
 2
36ν 2
36ν 2 w f = ( s − 1) gd 
+
−
(6)

3
( s − 1) gd 3  3 ( s − 1) gd
where ν denotes the kinetic viscosity of water.

2.5 BEACH MORPHOLOGICAL MODELS WITH SUSPENDED SEDIMENT
2.5.1 Field Measurements of Suspended Sediment and Comparison with CERC Formula
Equation 5 by Bailard (1984) for the K value of the CERC formula suggests the enhanced role ofsuspended sediment on longshore transport. His revision of the coefficient value for the bed load
efficiency factor eb from 0.21 to 0.12 and that of suspended load efficiency factor es from 0.025
to 0.032, when he derived Eq. 5, indicates an increased role of suspended sediment. If one
assumes the condition of α b = 10 degrees, Hb = 3.0 m at the depth hb = 4.0 m, and the mean
diameter of d = 0.2 mm (wf = 2.4 cm/s), the sum of the first two terms in the right-hand side of Eq.
5 becomes 0.18 and the third term has the value of 0.29 (ub is assumed equal to ghb ). If theformer is regarded to represent the contribution of the bed load and the latter as that of suspendedload, it is evident that the suspended load becomes dominant in the longshore transport of finesediment for most of storm conditions.
Direct comparison between the contributions by the bed load and by the suspended load
across the beach is difficult, because the field measurement of bed load transport is almost
impossible. Although tracer investigations provide the data of local longshore transport rate, wecannot tell whether tracers were transported by the bed load mode or suspended mode. What we
can do is to estimate the amount of suspended sediment transport rate by integrating themeasured data of sediment concentrations and current velocities across the surf zone and tocompare the result with an estimate of total sediment transport rate.
The objective of field measurements by Kana and Ward (1980) was to estimate the sediment